Quasi-random Number Generator Research Articles

Three-dimensional strain descriptors at the Earth’s surface through 3D retrieved co-event displacement fields of differential interferometric synthetic aperture radar

In deformation analysis, invariant strain descriptors that are independent of the coordinate system are significant. An approach is proposed to determine the strain tensor and invariant strain quantities through the 3D retrieved co-event displacement of differential interferometric synthetic aperture radar (DInSAR). An optimal cell count is selected based on the proposed rule-of-thumb formula. This set of coherent cells with prescribed acceptable minimum value coherence is distributed on the domain through a quasi-random number generator. The recursive moving least squares method is applied to estimate the components of strain and differential rotation tensors. In practice, this method is not limited to the homogeneous strain field hypothesis. The objective here is to propose an approach to determine the local and regional strain patterns in SAR’s image resolution details. This approach is tested on both synthetic and real data. The real data consist of 3D displacements of 19 global navigation satellite system stations and SAR images of Kilauea Volcano eruption in July 2007. Results indicate that the areas with maximum shear strain and maximum dilatation are located exactly near the east rift zone of the volcano.

New deterministic initialization method for soft computing global optimization algorithms

<span>The initialization stage12 of a Soft Computing (SC) algorithm is vital as it affects the success rate of algorithms in solving multi-peak global optimization problems. The individuals in an initial population, which are known as search agents, are often generated randomly using pseudo-random number generator (PRNG) due to unavailability of prior information on the location of global peak (GP). The random nature of the generated search agents causes uneven distribution of the initial population over the search space (SS), which may lead the search towards unpromising regions from the very beginning. This paper proposes a new deterministic initialization method (DIM) for SC algorithms where search agents are evenly fixed in the SS by using a simple deterministic formulation. The performance of the proposed DIM is then compared to the conventional PRNG and more recent quasi-random number generator (QRNG). An optimization case study is carried out using two popular SC algorithms which are the Particle Swarm Algorithm (PSO) and the Evolutionary Programming (EP), and three relatively new SC algorithms which are the Whale Optimization Algorithm (WOA), the Elephant Herding Optimization (EHO), and the Butterfly Optimization Algorithm (BOA). The optimization is done on various one-dimensional (1D) benchmark functions, as well as practical problems such as partial shading condition (PSC). Simulation results show that the proposed DIM successfully improved the performance of each SC algorithm under study in solving almost all tested functions with 99% success rate compared to 88.7% and 80.2% for the QRNG and PRNG approaches respectively. Furthermore, the WOA is the most reliable and robust among the five SC techniques under study with a success </span>

Self-organizing maps for pattern recognition in design of alloys

ABSTRACTA combined experimental–computational methodology for accelerated design of AlNiCo-type permanent magnetic alloys is presented with the objective of simultaneously extremizing several magnetic properties. Chemical concentrations of eight alloying elements were initially generated using a quasi-random number generator so as to achieve a uniform distribution in the design variable space. It was followed by manufacture and experimental evaluation of these alloys using an identical thermo-magnetic protocol. These experimental data were used to develop meta-models capable of directly relating the chemical composition with desired macroscopic properties of the alloys. These properties were simultaneously optimized to predict chemical compositions that result in improvement of properties. These data were further utilized to discover various correlations within the experimental dataset by using several concepts of artificial intelligence. In this work, an unsupervised neural network known as self-organizing maps was used to discover various patterns reported in the literature. These maps were also used to screen the composition of the next set of alloys to be manufactured and tested in the next iterative cycle. Several of these Pareto-optimized predictions out-performed the initial batch of alloys. This approach helps significantly reducing the time and the number of alloys needed in the alloy development process.

Probabilistic power flow calculation using the Johnson system and Sobol's quasi‐random numbers

This study puts forward a probabilistic power flow calculation method based on the Johnson system and Sobol's quasi-random numbers. The Johnson system is utilised to simulate the distribution function of one dimensional variable and model the correlation of multiple uncertainties with historical data of the uncertainties. The improved Sobol's quasi-random number generator is adopted to produce the low-discrepancy samples in Monte Carlo simulation. The accuracy of the Johnson system is compared with other modelling methods of uncertainties and the comparison of Sobol's quasi-random numbers and other techniques, such as Latin hypercube sampling and simple random sampling are presented for the cases of IEEE 30-bus system and IEEE 118-bus system.

Optimal Halton Sequence via Inversive Scrambling

In this article, we develop the Halton sequence of generating quasi-random numbers to an optimal sequence which has the inversive property. The new constructed quasi-random number generator satisfies the extra uniformity condition on [0, 1]. We finally present the performances of this generator in contrast to the former optimal Halton sequence in Chi et al. (2005) and modified optimal Halton sequence in Fathi et al. (2009).

Monte Carlo methods in fuzzy queuing theory

In this paper, we consider an optimization problem in fuzzy queuing theory that was first used in web planning. This fuzzy optimization problem has no solution algorithm and approximate solutions were first produced by computing the fuzzy value of the objective function for only sixteen values of the fuzzy variables. We introduce our fuzzy Monte Carlo method, using a quasi-random number generator, to produce 100,000 random sequences of fuzzy vectors for the fuzzy variables, which will present a much better approximate solution.

MONTE CARLO METHODS IN FUZZY NON-LINEAR REGRESSION

We apply our new fuzzy Monte Carlo method to certain fuzzy non-linear regression problems to estimate the best solution. The best solution is a vector of triangular fuzzy numbers, for the fuzzy coefficients in the model, which minimizes an error measure. We use a quasi-random number generator to produce random sequences of these fuzzy vectors which uniformly fill the search space. We consider example problems to show that this Monte Carlo method obtains solutions comparable to those obtained by an evolutionary algorithm.

Monte Carlo methods in fuzzy linear regression II

We apply our new fuzzy Monte Carlo method to a certain fuzzy linear regression problem to estimate the best solution. The best solution is a vector of crisp numbers, for the coefficients in the model, which minimizes one of two error measures. We use a quasi-random number generator to produce random sequences of these crisp vectors which uniformly fill the search space. We consider an example problem and show this Monte Carlo method obtains the best solution for both error measures.

Generating parallel quasirandom sequences via randomization

Quasi-Monte Carlo (QMC) methods are now widely used in scientific computation, especially in estimating integrals over multidimensional domains. One advantage of QMC is that it is easy to parallelize applications, and so the success of any parallel QMC application depends crucially on the quality of parallel quasirandom sequences used. Much of the recent work dealing with parallel QMC methods has been aimed at splitting a single quasirandom sequence into many subsequences. In contrast with this perspective to concentrate on breaking one sequence up, this paper proposes an alternative approach to generating parallel sequences for QMC. This method generates parallel sequences of quasirandom numbers via scrambling. The exact meaning of scrambling depends on the type of parallel quasirandom numbers. In general, we seek to randomize the generator matrix for each quasirandom number generator. Specifically, this paper will discuss how to parallelize the Halton sequence via scrambling. The proposed scheme for generating parallel random number streams is especially good for heterogeneous and unreliable computing environments.

An Efficient Randomized Quasi-Monte Carlo Algorithm for the Pareto Distribution

This paper studies a new randomized quasi-Monte Carlo method for estimating the mean and variance of the Pareto distribution. In many Monte Carlo simulations, there are some stability problems for estimating the population Pareto variance by using the sample variance. In this paper, we propose a randomized quasi-random number generator [quasi- RNG] to generate Pareto random samples, such that the sample mean and sample variance estimators gain more efficiency. The efficiency of this generator relative to the popular linear congruential random number generator [LC-RNG] is studied by using the simulation mean square errors. We also compare the results of the Kolmogorov-Smirnov goodness-of-fit tests using these two sample generators.

Using Quasirandom Weights in Neural Networks

ABSTRACTWe present a novel training algorithm for a feed forward neural network with a single hidden layer of nodes (i.e., two layers of connection weights). Our algorithm is capable of training networks for hard problems, such as the classic two-spirals problem. The weights in the first layer are determined using a quasirandom number generator. These weights are frozen—they are never modified during the training process. The second layer of weights is trained as a simple linear discriminator using methods such as the pseudoinverse, with possible iterations. We also study the problem of reducing the hidden layer: pruning low-weight nodes and a genetic algorithm search for good subsets.

Randomness versus deterministic chaos: Effect on invasion percolation clusters.

What is the difference between randomness and chaos ? Although one can define randomness and one can define chaos, one cannot easily assess the difference in a practical situation. Here we compare the results of these two antipodal approaches on a specific example. Specifically, we study how well the logistic map in its chaotic regime can be used as quasirandom number generator by calculating pertinent properties of a well-known random process: invasion percolation. Only if \ensuremath{\lambda}>${\ensuremath{\lambda}}_{1}^{\mathrm{*}}$ (the first reverse bifurcation point) is a smooth extrapolation in system size possible, and percolation exponents are retrieved. If \ensuremath{\lambda}\ensuremath{\ne}1, a sequential filling of the lattice with the random numbers generates a measurable anisotropy in the growth sequence of the clusters, due to short-range correlations.

A quasi-random number generator with infinite period

An aperiodic quasi-random number generator is constructed.